On estimands arising from misspecified semiparametric rate-based analysis of recurrent episodic conditions

Marginal rate-based analyses are widely used for the analysis of recurrent events in clinical trials. In many areas of application, the events are not instantaneous but rather signal the onset of a symptomatic episode representing a recurrent infection, respiratory exacerbation, or bout of acute depression. In rate-based analyses, it is unclear how to best handle the time during which individuals are experiencing symptoms and hence are not at risk. We derive the limiting value of the Nelson-Aalen estimator and estimators of the regression coefficients under a semiparametric rate-based model in terms of an underlying two-state process. We investigate the impact of the distribution of the episode durations, heterogeneity, and dependence on the asymptotic and finite sample properties of standard estimators. We also consider the impact of these features on power in trials designed to test intervention effects on rate functions. An application to a trial of individuals with herpes simplex virus is given for illustration.